# Geometry

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1. a=a
reflexive property
2. if a=b then b=a
symmetric property
3. if a=b and b=c, then a=c
transitive property
4. if a =b, then a+c = b+c
5. if a=b, then a-c= b-c
subtraction property of equality
6. if a=b, then a times c= b times c

AxC = BxC
multiplication property of equality
7. if a=b, then a/c=b/c

(c does not equal 0)
division property of equality
8. if a=b, then you may replace b with a in any expression
substitution property of equality
9. a(b+c)=ab+ac
distribution property
10. Through any 2 points, there is exactly one line
postulate 2-1
11. Through any 3 collinear points there is exactly 1 plane.
Postulate 2-2
12. A line contains at least 2 points
Postulate 2-3
13. A plane contains at least 3 points, not all on the same line
Postulate 2-4
14. If 2 points lie on a plane then the entire line containing those 2 points lies in that plane
Postulate 2-5
15. Two lines intersect in a line
Postulate 2-6
16. Two planes intersect in a line
Postulate 2-7
17. IF M is midpoint of segment AB, then segment AM is congruent to segment MB
Midpoint theorem
18. The points on any line or line segment can be paired with real numbers so that, given any 2 points, A and B on a line, A corresponds to zero, and B corresponds to a positive real number
Ruler Postulate
19. If A, B, and C are collinear and B is between A and C, then AB+BC= AC. If AB+BC=AC, then B is between A and C.